Setup Outlook application to use custom email that is created on Skype's site

Question

I am trying to add an email Account on Outlook application (Windows 10) that came with my Office 365 subscription. But it throws the "Something wrong" error:

"Something went wrong and Outlook couldn't set up your account. Please try again..."

These are the steps used to create my custom email:

1. I own a domain (say example.com) and I created an account [e-mail] on that domain.

2. Wanted to use the above created email account on Skype so I went to skype's site and signed up using the Use your email instead option.

3. All well and good, Skype working with the new account etc. I then browse to outlook.com and use the same email address above to log in. Logged in successfully, opening the Outlook Mail site.

4. Now I try to setup the Outlook application using the same email address and I am returned with the error above. I then googled and found that I need to "enable" POP/IMAP on Outlook (Settings > Sync) and use the settings from the site to configure the application. I did and tried both POP and then IMAP option in Outlook app setup but the password screen keeps popping up and it doesn't go any further than that.

5. Used a couple of guides online but nothing has worked so far.

What am I missing and how can I resolve this error?

I also noticed that if I go straight to Outlook's site and Sign up for a new account, there is not an option to create an account from an email instead (like on skype's site). I did not understand why it is not possible on this site and on the other (skype) it is.

Also, when I create a custom email on my domain/hosting panel with its own mailbox then I send an email from another account to this email, it is only visible in my own mailbox and not in Outlook's Mail box, why is that?

EDIT:

For my issue, I ended up using the pop/smtp settings of the domain/hosting provider (e.g. mail.example.com) rather than the ones Outlook provides. I started receiving and able to send emails from Outlook after this change.

Also, reading @Aidan's comment and the change about the App password tells me the password prompt issue could be because of that but I did not see any reason to setup the Outlook email now after I saw that I do not receive any email in the Outlook inbox after sending to [e-mail].

So, the question regarding why I do not receive emails in the Outlook inbox and keep receiving normally on my domain's mailbox still stands if anyone could shed some light. Even though I am able to send an email from Outlook inbox (web) using [e-mail].